Some Results On Quasi-thin Scheme

In this thesis,we study the schurity and separability problem of a certain type of scheme called the quasi-thin scheme.The main results are:· Let X =(Ω,S)be a Quasi-thin scheme.If X has only one orthogonal and this orthogonal is thin,then any point extension of Xα is 1-regular if and only if the action of S1 on S2 by right multiplication is transitive.in this case,|S2|＝|S1|/2.· Let T ＝｛u,v,w} be a non-exceptional triangle of a quasi-thin scheme X =(Ω,S).Then there exist relations a∈u*w and b∈w*v for which |ab∩u*v|=1.· Given a quasi-thin scheme X ＝(Ω,S);α∈Ω.If X contains exactly one orthognal u,and u is thick,then:X≌XαS1(?)XαT,(?)α∈Ω.· Any commutative klein scheme is schurian.